Basic properties
| Modulus: | \(8112\) | |
| Conductor: | \(507\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{507}(161,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8112.ee
\(\chi_{8112}(161,\cdot)\) \(\chi_{8112}(593,\cdot)\) \(\chi_{8112}(785,\cdot)\) \(\chi_{8112}(1217,\cdot)\) \(\chi_{8112}(1409,\cdot)\) \(\chi_{8112}(1841,\cdot)\) \(\chi_{8112}(2033,\cdot)\) \(\chi_{8112}(2657,\cdot)\) \(\chi_{8112}(3089,\cdot)\) \(\chi_{8112}(3713,\cdot)\) \(\chi_{8112}(3905,\cdot)\) \(\chi_{8112}(4337,\cdot)\) \(\chi_{8112}(4529,\cdot)\) \(\chi_{8112}(4961,\cdot)\) \(\chi_{8112}(5153,\cdot)\) \(\chi_{8112}(5585,\cdot)\) \(\chi_{8112}(5777,\cdot)\) \(\chi_{8112}(6209,\cdot)\) \(\chi_{8112}(6401,\cdot)\) \(\chi_{8112}(6833,\cdot)\) \(\chi_{8112}(7025,\cdot)\) \(\chi_{8112}(7457,\cdot)\) \(\chi_{8112}(7649,\cdot)\) \(\chi_{8112}(8081,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((5071,6085,2705,3889)\) → \((1,1,-1,e\left(\frac{27}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 8112 }(161, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(-i\) | \(1\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{19}{26}\right)\) |